Fréchet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables.

Fr\'echet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables. However, its practical applicability has been hindered by its reliance on ideal scenarios with abundant and noiseless covariate data. In this paper, we present a novel estimation method that tackles these limitations by leveraging the low-rank structure inherent in the covariate matrix. Our proposed framework combines the concepts of global Fr\'echet regression and principal component regression, aiming to improve the efficiency and accuracy of the regression estimator. By incorporating the low-rank structure, our method enables more effective modeling and estimation, particularly in high-dimensional and errors-in-variables regression settings. We provide a theoretical analysis of the proposed estimator's large-sample properties, including a comprehensive rate analysis of bias, variance, and additional variations due to measurement errors. Furthermore, our numerical experiments provide empirical evidence that supports the theoretical findings, demonstrating the superior performance of our approach. Overall, this work introduces a promising framework for regression analysis of non-Euclidean variables, effectively addressing the challenges associated with limited and noisy covariate data, with potential applications in diverse fields.

Artificial neural networks (ANNs) are increasingly powerful models of brain computation, yet it remains unclear whether improving their task performance also makes their internal representations more similar to brain signals. To address this question in the auditory domain, we quantified the alignment between the internal representations of 36 different audio models and brain activity from two independent fMRI datasets. Using voxel-wise and component-wise regression, and representation similarity analysis (RSA), we found that recent self-supervised audio models with strong performance in diverse downstream tasks are better predictors of auditory cortex activity than older and more specialized models. To assess the quality of the audio representations, we evaluated these models in 6 auditory tasks from the HEAREval benchmark, spanning music, speech, and environmental sounds. This revealed strong positive Pearson correlations ($r>0.7$) between a model's overall task performance and its alignment with brain representations. Finally, we analyzed the evolution of the similarity between audio and brain representations during the pretraining of EnCodecMAE. We discovered that brain similarity increases progressively and emerges early during pretraining, despite the model not being explicitly optimized for this objective. This suggests that brain-like representations can be an emergent byproduct of learning to reconstruct missing information from naturalistic audio data.

The ascension of social media platforms has transformed our understanding of urban environments, giving rise to nuanced variations in sentiment reaction embedded within human perception and opinion, and challenging existing multidimensional sentiment analysis approaches in urban studies. This study presents novel methodologies for identifying and elucidating sentiment inconsistency, constructing a dataset encompassing 140,750 Baidu and Tencent Street view images to measure perceptions, and 984,024 Weibo social media text posts to measure opinions. A reaction index is developed, integrating object detection and natural language processing techniques to classify sentiment in Beijing Second Ring for 2016 and 2022. Classified sentiment reaction is analysed and visualized using regression analysis, image segmentation, and word frequency based on land-use distribution to discern underlying factors. The perception affective reaction trend map reveals a shift toward more evenly distributed positive sentiment, while the opinion affective reaction trend map shows more extreme changes. Our mismatch map indicates significant disparities between the sentiments of human perception and opinion of urban areas over the years. Changes in sentiment reactions have significant relationships with elements such as dense buildings and pedestrian presence. Our inconsistent maps present perception and opinion sentiments before and after the pandemic and offer potential explanations and directions for environmental management, in formulating strategies for urban renewal.

Fréchet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables.

GNN architecture that is universally effective across a wide range of graph machine learning tasks.

In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline the complex and time-consuming traditional manual process of discovering scientific laws, helping us gain insights into fundamental issues in modern science. In this work, we introduce a pre-trained symbolic foundation regressor that can effectively compress complex data with numerous interacting variables while producing interpretable physical representations. Our model has been rigorously tested on non-network symbolic regression, symbolic regression on complex networks, and the inference of network dynamics across various domains, including physics, biochemistry, ecology, and epidemiology. The results indicate a remarkable improvement in equation inference efficiency, being three times more effective than baseline approaches while maintaining accurate predictions. Furthermore, we apply our model to uncover more intuitive laws of interaction transmission from global epidemic outbreak data, achieving optimal data fitting. This model extends the application boundary of pre-trained symbolic regression models to complex networks, and we believe it provides a foundational solution for revealing the hidden mechanisms behind changes in complex phenomena, enhancing interpretability, and inspiring further scientific discoveries.